Prove that: `2s in^2pi/6+cos e c^2(7pi)/6cos^2pi/3=3/2`

Explanation

To prove that \( 2 \sin^2 \frac{\pi}{6} + \cos^2 \left( \frac{7\pi}{6} \right) \cos^2 \left( \frac{\pi}{3} \right) = \frac{3}{2} \), we will evaluate the left-hand side (LHS) step by step.

### Step 1: Evaluate \( \sin^2 \frac{\pi}{6} \)
We know that:
\[ \sin \frac{\pi}{6} = \frac{1}{2} \]
Thus,
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